Confined Electron: Min Uncertainty in Momentum/Velocity

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SUMMARY

The discussion focuses on calculating the minimum uncertainty in the momentum and velocity of an electron confined to a quantum wire of length 150 nm. The uncertainty principle is applied, specifically the relation that states the product of the uncertainties in position and momentum must be greater than or equal to \( \frac{h}{4\pi} \). The user initially calculated the uncertainty in momentum as \( 3.52 \times 10^{-28} \) but recognized this value as incorrect. The correct approach involves using the proper formulation of the uncertainty principle with Planck's constant.

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Homework Statement


An electron is confined to a "quantum wire" of length 150 nm. what is the minimum uncertainty in the electron's momentum component along the length of the wire? What is the minimum uncertainty in the electron's velocity component along the length of the wire?


Homework Equations


(uncertainty in x coordinate of position)(uncertainty in x component of momentum) > or equal to 1/2pi

I used 150 x 10^-9 for change in x and solved but got 3.52 x 10^-28 but this is wrong

how do i do this? thanks

The Attempt at a Solution

 
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(uncertainty in x coordinate of position)(uncertainty in x component of momentum) > or equal to 1/2pi ?

isn't it h/2pi ?
 

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